Average Error: 6.2 → 2.5
Time: 6.8s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.8095903151115152 \cdot 10^{-138}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;z \le 6.9390753974297484 \cdot 10^{-149}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - t}{\frac{a}{y}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.8095903151115152 \cdot 10^{-138}:\\
\;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\

\mathbf{elif}\;z \le 6.9390753974297484 \cdot 10^{-149}:\\
\;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\

\mathbf{else}:\\
\;\;\;\;x - \frac{z - t}{\frac{a}{y}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r412854 = x;
        double r412855 = y;
        double r412856 = z;
        double r412857 = t;
        double r412858 = r412856 - r412857;
        double r412859 = r412855 * r412858;
        double r412860 = a;
        double r412861 = r412859 / r412860;
        double r412862 = r412854 - r412861;
        return r412862;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r412863 = z;
        double r412864 = -1.8095903151115152e-138;
        bool r412865 = r412863 <= r412864;
        double r412866 = x;
        double r412867 = y;
        double r412868 = a;
        double r412869 = r412867 / r412868;
        double r412870 = t;
        double r412871 = r412863 - r412870;
        double r412872 = r412869 * r412871;
        double r412873 = r412866 - r412872;
        double r412874 = 6.939075397429748e-149;
        bool r412875 = r412863 <= r412874;
        double r412876 = r412868 / r412871;
        double r412877 = r412867 / r412876;
        double r412878 = r412866 - r412877;
        double r412879 = r412868 / r412867;
        double r412880 = r412871 / r412879;
        double r412881 = r412866 - r412880;
        double r412882 = r412875 ? r412878 : r412881;
        double r412883 = r412865 ? r412873 : r412882;
        return r412883;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.2
Target0.7
Herbie2.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -1.8095903151115152e-138

    1. Initial program 7.4

      \[x - \frac{y \cdot \left(z - t\right)}{a}\]
    2. Using strategy rm

    3. Applied associate-/l*6.1

      \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{z - t}}}\]
    4. Using strategy rm

    5. Applied associate-/r/2.1

      \[\leadsto x - \color{blue}{\frac{y}{a} \cdot \left(z - t\right)}\]

    if -1.8095903151115152e-138 < z < 6.939075397429748e-149

    1. Initial program 4.3

      \[x - \frac{y \cdot \left(z - t\right)}{a}\]
    2. Using strategy rm

    3. Applied associate-/l*3.3

      \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{z - t}}}\]

    if 6.939075397429748e-149 < z

    1. Initial program 6.5

      \[x - \frac{y \cdot \left(z - t\right)}{a}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity6.5

      \[\leadsto x - \color{blue}{1 \cdot \frac{y \cdot \left(z - t\right)}{a}}\]

    4. Applied *-un-lft-identity6.5

      \[\leadsto \color{blue}{1 \cdot x} - 1 \cdot \frac{y \cdot \left(z - t\right)}{a}\]

    5. Applied distribute-lft-out--6.5

      \[\leadsto \color{blue}{1 \cdot \left(x - \frac{y \cdot \left(z - t\right)}{a}\right)}\]

    6. Simplified2.2

      \[\leadsto 1 \cdot \color{blue}{\left(x - \frac{z - t}{\frac{a}{y}}\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.8095903151115152 \cdot 10^{-138}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;z \le 6.9390753974297484 \cdot 10^{-149}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - t}{\frac{a}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

  (- x (/ (* y (- z t)) a)))